APPLICATION OF NUMERICAL CONTINUATION AND
BIFURCATION METHODS TO THE LONG JOURNAL BEARING
PROBLEM IN THE PRESENCE AND ABSENCE OF CAVITATION
INSTITUTO NACIONAL DE PESQUISAS ESPACIAIS
DIVISÃO DE MECÂNICA ESPACIAL E CONTROLE
MÁRIO CÉSAR RICCI
Av. dos Astronautas, 1758 - Jardim da Granja
Cxa. Postal - 515 CEP - 12.201-970
12.227-010 - SÃO JOSÉ DOS CAMPOS - S.P.
e-mail: [email protected]
In the mechanical engineering moving system's field the radial journal bearing is one of
the great interests. This work deals with the Reynolds approximation or the long bearing
as an autonomous, unforced and balanced-mass rotor system. Two cases are studied: a)
without cavitation and b) with the π-film cavitation. The system can be described by a
set of four first order nonlinear ordinary differential equations whose fluid forces are
approximate solutions of partial differential equations. Rigorous geometrical constraints
are imposing on the movement of the rotor’s center around stator’s center to avoid the
contact between them. Otherwise, the contact could well result in bearing failure. The
work uses numerical methods for bifurcation problems to calculate Hopf bifurcation
points and numerical continuation methods to obtain branching of periodic orbits that
emanate from stationary solutions. Trajectories of the rotor’s center are shown. The
half-frequency whirl is studied. Test functions as an indication of bifurcation are shown.
A bifurcation diagram is shown for the case a). For the case b) the amplitude and
frequency of periodic solutions as a function of rotor’s angular velocity for low,
medium and high loads are shown. A limit stability curve is proposed.